Q.Find the sum to infinity of the G.P. $8 + 4 + 2 + 1 + \ldots$

[!TLDR] This is a G.P. with $a=8,r=\tfrac12$; since $|r|<1$, apply $S_\infty=\dfra …

The series $8+4+2+1+\cdots$ is a G.P. with first term $a=8$ and common ratio $r=\dfrac{4}{8}=\dfrac12$. Since $|r|=\dfrac12<1$, the sum to infinity exists and is given by $S_\infty=\dfr …

Identify $a$ and $r$, check $|r|<1$ so the infinite sum exists, then apply $ …

Quoting $S_\infty=\frac a{1-r}$ without first checking $|r|<1$ is a serious conceptual error — the formula is meaningles …